Hierarchical Aggregation for Numerical Data under Local Differential Privacy

The proposal of local differential privacy solves the problem that the data collector must be trusted in centralized differential privacy models. The statistical analysis of numerical data under local differential privacy has been widely studied by many scholars. However, in real-world scenarios, numerical data from the same category but in different ranges frequently require different levels of privacy protection. We propose a hierarchical aggregation framework for numerical data under local differential privacy. In this framework, the privacy data in different ranges are assigned different privacy levels and then disturbed hierarchically and locally. After receiving users’ data, the aggregator perturbs the privacy data again to convert the low-level data into high-level data to increase the privacy data at each privacy level so as to improve the accuracy of the statistical analysis. Through theoretical analysis, it was proved that this framework meets the requirements of local differential privacy and that its final mean estimation result is unbiased. The proposed framework is combined with mini-batch stochastic gradient descent to complete the linear regression task. Sufficient experiments both on synthetic datasets and real datasets show that the framework has a higher accuracy than the existing methods in both mean estimation and mini-batch stochastic gradient descent experiments.